8. Let K be an integer greater than 4 such that K+2, K+4, K+8,
and K+10 are all prime. What is the greatest integer that
is ALWAYS a factor of K+6?

9. Let M be the least common multiple of all the consecutive
integers 10 through 30, inclusive. Let N be the least
common multiple of M, 32, 33, 34, 35, 36, 38, 39, and 40.
What is the value of N divided by M?

10. For any positive integer G, what is the greatest common
divisor of 2G+1 and 2G+5?

11. What is the least positive integer N such that 450N is a
perfect cube?

12. Let S1 be the set of all positive multiples of 2 that are less
than 101. Then, let S2 be the set of all positive multiples
of 3 that are also less than 101. Finally, let S3 be the set
of all positive multiples of 5 that are less than 101. What
is the sum of all the numbers occurring in all three sets?

13. What is the least multiple of 14 whose digital sum is 14?

14. 144, being a multiple of itself, naturally ends with ...144.
What is the next greater multiple of 144 ending in ...144?

15. What is the only ordered triple {a,b,c} such that 6a+9b+20c=61,
where a, b, and c are positive whole numbers only?

16. x, y, and z are three consecutive whole numbers whose sum is
odd. Let P be the product of x, y, and z, and let M be the
least common multiple of x, y, and z. What is the ratio of
M to P? Express in simplest a/b form.

17. Express 9991 as the product of its prime factors.

18. Let abc be a 3-digit whole number, where a, b, and c are
its digits, not necessarily different. If nine times abc
is 1abc, what number is abc?